WORD PROBLEMS INVOLVING PERCENTAGE

Problem 1 :

A shop sells 200 chocolate, Vannila and strawberry ice creams. 45% of the ice creams sold are Vannila, and 30% are Strawberry. How many chocolate ice creams are sold ?

Solution :

Let us consider the given quantity as 100%.

200 = 100%

45% of ice creams are Vannila, 30% of ice creams are Strawberry.

Percentage of chocolate ice creams sold = 100 - (45 + 30)

= 100 - 75

= 25%

Number of chocolate ice creams = 25% of 200

= 0.25(200)

= 50

Problem 2 :

An animal park has lions, tigers and Zebras. 20% of the animals are lions and half of the animals are Zebras. If there are 120 animals at the park how many tigers are there ?

Solution :

Total number of animals = 120 = 100%.

20% of them are lions.

Half of them = 50% of the animals are Zebra.

Percentage of animals which are tiger = 100 - (20 + 50)

= 100 - 70

= 30%

30% of the animals are tigers.

Number of tigers = 30% of 120

= 0.30(120)

= 36

Problem 3 :

LA Galaxy have won 36% of their soccer matches, if they have played 50 matches, how many have they won ?

Solution :

Total number of matches they played = 50

Number of matches they won = 36% of the matches

= 36% of 50

= 0.36 (50)

= 18

So, they won 18 matches.

Problem 4 :

A car can travel 400 miles on a full tank of petrol. A more efficient car can travel 30% further. How many miles can it travel on a tank ?

Solution :

Distance covered by the car using full tank of petrol = 400 miles

400 miles = 100% of the distance

100 + 30 = 130% of 400

= 1.30 (400)

= 520 miles

So the efficient car can cover 520 miles.

Problem 5 :

In a fruit survey, 60 children choose their favourite  fruit out of the apples, bananas and watermelon. 30% of chose apples, 25% chose bananas. How many children chose watermelon ?

Solution :

Total number of children = 60 = 100%

Percentage of children who choose watermelon

= 100 - (30 + 25)

= 100 - 55

= 45%

Number of children who choose watermelon = 45% of 60

= 0.45(60)

= 27

So, 27 children choose watermelon.

Problem 6 :

In a traffic survey of 200 vehicles, bikes, buses and cars were recorded. 3/4 of the vehicles were cars and 17% were buses. How many bikes were there ?

Solution :

Total number of vehicles participated in the survey = 200

100% = 200 chocolates

3/4 of the vehicles = 75% of vehicles are cars.

Percentage of buses = 17%

Percentage of vehicles which are bikes = 100 - (75 + 17)

= 100 - 92

= 8%

8% of bikes are there.

Number of bikes = 8% of 200

= 0.08(200)

= 16

Problem 7 :

The bar graph shows a softball player’s home run totals. What was the percent of change from 2007 to 2008?

Solution :

Number of home runs in 2007 = 28

Number of home runs in 2008 = 20

Percentage change = [(28 - 20) / 28] x 100%

= (8/28) x 100%

= 0.285 x 100%

= 28.5%

So, homeruns decreased by 29 % approcimately.

Problem 8 :

You have 250 songs on your MP3 player. You delete 20% of the songs. How many songs are left?

a)  50     b)  150      c)  200   d) 300

Solution :

Total number of songs = 250

Percentage of songs deleted = 20%

Percentage of songs left = 80%

Number of songs left = 80% of 250

= 0.80(250)

= 200

So, option c is correct.

Problem 9 :

Suppose the length and width of the sandbox are doubled.

a. Find the percent of change in the perimeter.

b. Find the percent of change in the area.

Solution :

Length = 10 ft and width = 6 ft

Area of sandbox = 10 x 6

= 60 ft²

Perimter of sand box = 2(10 + 6)

= 2(16)

= 32 ft

When dimensions are doubled :

Length = 20 ft and width = 12 ft

Area of sand box = 20 x 12

= 240 ft²

Perimeter of sand box = 2(20 + 12)

= 2(32)

= 64 ft

a) Percentage change in perimeter = (64 - 32)/32 x 100%

= (32/32) x 100%

Increase = 100%

b) Percentage change in area = (240 - 60) / 60 x 100%

= (180/60) x 100%

= 3 x 100%

Increase = 300%

Problem 10 :

Donations to an annual fundraiser are 15% greater this year than last year. Last year, donations were 10% greater than the year before. The amount raised this year is $10,120. How much was raised 2 years ago?

Solution :

Let x be the fund 2 years ago.

Fund raised last year = 110% of x

Amount raised this year  $10120

115% of 110% of x = 10120

1.15(1.10) x = 10120

x = 10120/1.15(1.10)

= 8000

So, the amount raised 2 years ag is $8000.